Question

The motion of a body is given by the equation dv(t)/dt=6.0-3v(t),where v(t) is speed in m/s and t in sec.If body was at rest at t=0.

Answer 1

$\frac{dv}{dt} = 6-3v \\ \frac{dv}{6-3v} = dt \\ ln(6-3v)/(-3) = t + c$

At t=0, v=0
Therefore c = ln(6)

On simplifying it gives $v = 2(1-e^{-3t})$